Compare two unpaired samples, each with multiple proportions I have two samples of 20 households, one sample from each of two different areas; the data for each household is a) total adults in household and 2) adults with college education. 
Area 1

Household   Adults    College
1           2         1
2           1         0
3           4         1

...
Area 2

Household   Adults    College
1           3         1
2           2         2
3           4         2

...
I am interested in the proportion of adults per household who have college education and I want to know if this proportion is significantly different between the two areas. My question is: what test to use?
I can't use a standard test of equality of proportions because these require just the two pooled proportions for each area, which is begging the question. I suspect there is a lot of variance at the household level in both number of adults and proportion of college education, so this needs taking into account.
 A: In first place, please notice that your sample is very small and that reduces the power of any test you use. That is, no test will find a significative difference unless the differences in the samples are very big.
From your question I'm not sure about which is your variable of interest, but I assume it's proportion of people with college education in the adults of the same household, that is, the ratio between "college" and "adults" variables in your sample.
The question "if this proportion is different" can have several meanings, too.
Since your sample is tiny and assumptions of normality wouldn't be realistic, the ubiquitous independent samples t-test wouldn't be a good choice. Furthermore it just tests for difference on means, not difference of distributions.
Therefore, you should use a non-parametric equivalent of t-test as Mann–Whitney U test which doesn't make a normality assumption and tests for difference of distributions.
However, if you want to test equality of the total number of college educated people among the total number of adults in each population (that is college/adults), then a proportion test  could be useful - although your sample size is in the borderline of its usability.
